Many hate this response as population gives you more innovation. But the natural state of man is 0.5 per square mile. Consider the United States as 1000 miles by 3000 miles, that is 3 million square miles or a population of 1.5 million.
Without hybrid corn and crops we already would have a lot of famine. What is hybrid corn, it is where you take a corn and inbreed it to death and cross it with another inbred corn. The offspring, happens to be super corn.
Without that and modern machinery and genetically modified crops we already would be starving. Wheat production has triple per acre since 1961. Thus, next 100 years food security is probably safe. Safe at the expense of natural and wild foods.
http://igrow.org/agronomy/wheat/look...duction-in-sd/
The only thing that ultimately stops life is food and famine. Laws will be changed to make abortion illegal, then probably birth control. It will be a numbers game if you have 2 children you will be overrun by moral values of those that have 5-6 kids. If you don't have 5 kids you will probably have to pay double the tax. But, in the end the food runs out, then there is a war until the rebalance. Then we will be back track to have a major war every 50 years where 25-50% of the people die. What will be the result of the wars? To make birth control a capital offense!
The thing that might save us is space, where you can send the excess population. Mars is too far from the sun, but there will be greenhouses near Venus. People might live on Mars but get their food from Greenhouses. Evenutally people will learn to live a complete life without a planet. From there the whole galaxy is open, but eventually in the galaxy every ray of light will be used to make food for humans. Then the wars start again.